Weighted Multifractal Spectrum of V -Statistics
We analyze and describe the weighted multifractal spectrum of V-statistics. The description will be possible when the condition of “weighted saturation” is fulfilled. This means that the weighted topological entropy of the set of generic points of measure μ equals the measure-theoretic entropy of μ....
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| Autores principales: | , |
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| Formato: | Articulo |
| Lenguaje: | Inglés |
| Publicado: |
2020
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| Materias: | |
| Acceso en línea: | http://sedici.unlp.edu.ar/handle/10915/132509 |
| Aporte de: |
| Sumario: | We analyze and describe the weighted multifractal spectrum of V-statistics. The description will be possible when the condition of “weighted saturation” is fulfilled. This means that the weighted topological entropy of the set of generic points of measure μ equals the measure-theoretic entropy of μ. Zhao et al. (J Dyn Differ Equ 30:937–955, 2018) proved that for any ergodic measure weighted saturation is verified, generalizing a result of Bowen.
Here we prove that under a property of “weighted specification” the saturation holds for any measure. From this we obtain the description of the spectrum of V-statistics. This generalizes the variational result that Fan, Schmeling and Wu obtained for the non-weighted case. |
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